If a - b and c - d are perpendicular satisfying a - c - - b- d - - - 0 - a- d - 4- b- c - 9- then - is equal to

The correct option is D 6 We know that nbsp; (a × b).(c × d) = a· c amp; a· d b· c amp;b· d = λ amp; 4 9 amp;λ =λ^2 36 Since ...

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Standard XII

Mathematics

Applications of Dot Product

If a × b an...

Question

If $a \times b$ and $c \times d$ are perpendicular satisfying $a \cdot c = λ, b \cdot d = λ, (λ > 0), a \cdot d = 4, b \cdot c = 9$ , then $λ$ is equal to

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Solution

The correct option is D $6$
We know that $(a \times b) . (c \times d) = ∣ ∣ ∣ \begin{matrix} a \cdot c & a \cdot d b \cdot c & b \cdot d \end{matrix} ∣ ∣ ∣$
$= ∣ ∣ ∣ \begin{matrix} λ & 4 9 & λ \end{matrix} ∣ ∣ ∣ = λ^{2} - 36$
Since $a \times b$ and $c \times d$ are perpendicular so $λ^{2} - 36 = 0 \Rightarrow λ = \pm 6.$

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If a×b and c×d are perpendicular satisfying a⋅c=λ,b⋅d=λ,(λ>0), a⋅d=4,b⋅c=9, then λ is equal to

The correct option is D 6We know that (a×b).(c×d)=∣∣∣a⋅ca⋅db⋅cb⋅d∣∣∣=∣∣∣λ49λ∣∣∣=λ2−36Since a×b and c×d are perpendicular so λ2−36=0⇒λ=±6.

If $a \times b$ and $c \times d$ are perpendicular satisfying $a \cdot c = λ, b \cdot d = λ, (λ > 0), a \cdot d = 4, b \cdot c = 9$ , then $λ$ is equal to